If I remember correctly for odd n, it's regular, but for even n it gets interesting. I think there's a non-regular example for n=6. Victor On 1/9/09, Andy Latto <andy.latto@pobox.com> wrote:
On Fri, Jan 9, 2009 at 1:35 PM, victor miller <victorsmiller@gmail.com> wrote:
A few days ago, at the AMS meeting, I saw a neat talk by Michael Mossinghoff about "isodiametic" problems -- e.g. Fix the diameter of a conv ex n-gon and ask for the ones with maximum perimeter.
If this is an interesting problem, and calculating the result for n <= 500 is a worthwhile feat, then my intuition that the answer is always a regular polygon must be wrong. What is the smallest n for which the answer is not regular, and what does the resulting n-gon look like?
My guess is that the answer is n = 5. If so, could this be related somehow to the fact that if you want to find the minimum x such that 5 discs of diameter x cover a disc of diameter 1, the configuration of these discs that exhibits the minimum is not a 5-fold symmetric one.
-- Andy.Latto@pobox.com
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